/**
 * 64. 最小路径和
 */
public class Solution_64 {
    /**
     * 动态规划
     * <p>
     * 时间复杂度：O(MN)
     * 空间复杂度：O(MN)
     */
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) {
            return 0;
        }

        int m = grid.length, n = grid[0].length;
        // dp[i][j] 表示到达 (i,j) 的最小路径和
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        // dp 第一列
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        // dp 第一行
        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        // dp
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
            }
        }
        return dp[m - 1][n - 1];
    }

    public static void main(String[] args) {
        Solution_64 solution = new Solution_64();
        int[][] grid = { { 1, 3, 1 }, { 1, 5, 1 }, { 4, 2, 1 } };
        int ans = solution.minPathSum(grid);
        System.out.println(ans);
    }
}
